Question 74·Easy·Math

0 / 2000

The function $g$ is defined by $g(x)=3x^{2}-5$ . What is the value of $g(x)$ when $x=-2$ ?

For function-evaluation questions like this, immediately rewrite the function with the given input in parentheses (for example, $g(-2)=3(-2)^2-5$ ). Then apply the order of operations carefully: handle exponents first (remember that squaring a negative gives a positive), then multiply, and finally add or subtract. Writing each step clearly helps avoid sign errors and is usually faster and safer than trying to do everything mentally under time pressure.

Hints

Click me!

Start by using the function rule

Rewrite $g(x)=3x^{2}-5$ with $x$ replaced by $-2$ . What expression do you get for $g(-2)$ ?

Be careful with the exponent

When you see $(-2)^{2}$ , remember that you are multiplying $-2$ by itself. Is the result positive or negative?

Follow order of operations

After you square $-2$ , what do you do next: multiply by $3$ or subtract $5$ ? Do the operations step by step.

Desmos Guide

Define the function in Desmos

Type g(x) = 3x^2 - 5 into Desmos so it understands the function $g$ .

Evaluate the function at $x=-2$

In a new line, type g(-2) and look at the numerical output that Desmos shows. That number is the value of $g(x)$ when $x=-2$ .

Step-by-step Explanation

Substitute $x=-2$ into the function

The function is $g(x)=3x^{2}-5$ . To find $g(-2)$ , replace $x$ with $-2$ :

g(-2)=3(-2)^{2}-5

Be sure to keep $-2$ in parentheses when you square it.

Square the input

Now square $-2$ :

(-2)^{2}=4

Substitute this back into the expression:

g(-2)=3\cdot 4 - 5

Multiply before subtracting

Multiply $3$ and $4$ :

3\cdot 4 = 12

Now the expression becomes:

g(-2)=12-5

Subtract to get the final value

Finally, subtract $5$ from $12$ :

12-5=7

So, $g(-2)=7$ , which corresponds to choice C.

Question 74·Easy·Math

Strategy

Hints

Desmos Guide

Step-by-step Explanation

Study Hints

Strategy

Hints

Desmos Guide

Step-by-step Explanation